The Heliocentric ModelThe Heliocentric Model

Justin WalegaJustin Walega

In The Beginning…In The Beginning…

Geocentric ModelGeocentric Model SymmetrySymmetry PtolemyPtolemy

ImageryImagery

Why?Why?

Appeared all planets orbited regularlyAppeared all planets orbited regularly

Earth is stableEarth is stable

IssuesIssues

Dancing planetsDancing planets Epicycles – ApolloniusEpicycles – Apollonius

Early NamesEarly Names

PhilolausPhilolaus

AristarchusAristarchus

Archimedes – a larger universeArchimedes – a larger universe

Change?Change?

RegiomontanusRegiomontanus

ChristianityChristianity Calendar issues - EasterCalendar issues - Easter

CopernicusCopernicus

De revolutionibus orbium celestium - 1543De revolutionibus orbium celestium - 1543 (On the Revolutions of the Heavenly Spheres)(On the Revolutions of the Heavenly Spheres)

Gave mathematical description with Gave mathematical description with moving Earthmoving Earth

SpheresSpheres

What’s gravity?What’s gravity?

Simplest solutionSimplest solution

CopernicusCopernicus

Ptolemy’s methodsPtolemy’s methods

100,000 instead of 60100,000 instead of 60

ChordsChords

Methods of solvingMethods of solving Plane and spherical trianglesPlane and spherical triangles

Spherical TrianglesSpherical Triangles

““If in the same sphere two triangles have If in the same sphere two triangles have right angles and another angle equal to right angles and another angle equal to another angle and one side equal to one another angle and one side equal to one side – whether the sides be adjacent to side – whether the sides be adjacent to the equal angles or lie opposite one of the the equal angles or lie opposite one of the equal sides – they will have the remaining equal sides – they will have the remaining sides and the remaining angle equal to the sides and the remaining angle equal to the remaining angle.”remaining angle.”

New IssuesNew Issues

Copernicus – Sun not quite centerCopernicus – Sun not quite center

Protestant vs. Roman CatholicProtestant vs. Roman Catholic Chronicles 16:30: "the world also shall be Chronicles 16:30: "the world also shall be

stable, that it be not moved." stable, that it be not moved."

Used for calculations rather than accurateUsed for calculations rather than accurate

1717thth Century Century

Ancient IndiaAncient India

Aryabhata – Aryabhata – AryabhatiyaAryabhatiya Spinning axisSpinning axis Relation to SunRelation to Sun

Nilakantha SomayajiNilakantha Somayaji AryabhatiyabhasaAryabhatiyabhasa - commentary - commentary Planets around Sun around EarthPlanets around Sun around Earth

Same as Tycho Brahe’s modelSame as Tycho Brahe’s model

Islamic ViewsIslamic Views

Alhazen’s Alhazen’s Doubts on PtolemyDoubts on Ptolemy Questioned his detailsQuestioned his details Proposed axis rotationProposed axis rotation

Heliocentric concept abandoned multiple Heliocentric concept abandoned multiple timestimes

Tusi & Qushji – moving EarthTusi & Qushji – moving Earth

Never reached heliocentric modelNever reached heliocentric model

Advancing Through TimeAdvancing Through Time

Galileo – Galileo – Starry MessengerStarry Messenger (1610) (1610) TelescopeTelescope

Galileo’ dialogueGalileo’ dialogue

Kepler – elliptical orbitKepler – elliptical orbit EccentricityEccentricity

Earth’s EccentricityEarth’s Eccentricity

((ππ/4) x ( (186-179)/(186+179) ) ≈ 0.015/4) x ( (186-179)/(186+179) ) ≈ 0.015

186 days: March equinox -> Sept. equinox186 days: March equinox -> Sept. equinox

179 days: Sept. equinox -> March equinox179 days: Sept. equinox -> March equinox

The planetary orbit is an The planetary orbit is an ellipseellipse

The Sun is a The Sun is a focal pointfocal point, not the center, not the center

Neither the linear speed nor the angular speed of Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the the planet in the orbit is constant, but the area area

speedspeed is constant. is constant.

The square of the sidereal period is The square of the sidereal period is proportionate to the cube of the proportionate to the cube of the mean mean between the maximum and minimumbetween the maximum and minimum distances from the Sun.distances from the Sun.

PP is the orbital period of planet and is the orbital period of planet and aa is the is the semimajor axis of the orbit semimajor axis of the orbit

Recent TimesRecent Times

Not center of universeNot center of universe

Infinite? Position?Infinite? Position?